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LOCAL RINGS OVER WHICH ALL MODULES HAVE RATIONAL POINCAR
 

Summary: LOCAL RINGS OVER WHICH ALL MODULES
HAVE RATIONAL POINCAR 
E SERIES
Luchezar L. Avramov
To Steve Halperin on February 1
Abstract. If the homotopy Lie algebra   (R) of a local ring R contains a free Lie subalge-
bra of nite codimension, then for each nitely generated R{modules M the Poncare series
P R
M (t) =
P 1
n=0 dim k Tor R
n (M; k)  t n represents a rational function in t, and there is a least
common denominator for all these functions. When this denominator is a power of (1 t),
the ring R is a complete intersection, which has at most one non-quadratic de ning equation.
Introduction
Let R be a commutative noetherian local ring with maximal ideal mR and residue
eld k, and let M be a nitely generated R{module. An important characteristic of
M is contained in its Betti sequence f b R
n (M) = dim k Tor R
n (M; k) g n0 , which re nes the

  

Source: Avramov, Luchezar L.- Department of Mathematics, University of Nebraska-Lincoln

 

Collections: Mathematics